Which of the following expressions are polynomials in one variable and which are not? State reasons for your answer.
Which of the following expressions are polynomials in one variable and which are not? State reasons for your answer.
(i) 4x2 - 3x + 7
(ii) y2 + √2
(iii) 3√t + t√2
(iv) y + 2/y
(v) x10 + y3 + t50
Answer
(i) 4x2 - 3x + 7
There is only one variable x with whole number power so this polynomial in one variable.
(ii) y2 + √2
There is only one variable y with whole number power so this polynomial in one variable.
(iii) 3√2 + t√2
There is only one variable t but in 3√t power of t is 1/2 which is not a whole number so 3√t + t√2 is not a polynomial.
(iv) y + 2/y
There is only one variable y but 2/y = 2y-1 so the power is not a whole number so y + 2/y is not a polynomial.
(v) x10 + y3 + t50
There are three variable x, y and t and there powers are whole number so this polynomial in three variable.
